Development of a solution method for the differential equations arising in the biosphere module of the BNFL's suite of codes MONDRIAN

Abstract British Nuclear Fuels plc owns and operates the near-surface Drigg disposal facility for low level radioactive waste. The long-term performance of the site is modelled by a suite of computer codes called MONDRIAN. One of the modules of MONDRIAN deals with the transport of radionuclides through the environment, and this paper reports on the current status of this module (BIOS). We derive the basic set of working equations from first principles and show clearly how the approximate nature of the final equations is arrived at. This is done by an averaging process leading to compartments, in and out of which radionuclides, solids and water can flow. The equations allow radioactive decay chains and an arbitrary number of compartments. There is also the facility to deal with changes in the rate coefficients, thereby simulating different environmental states. It is also possible to include the creation of new compartments arising as a consequence of climatic variations. In addition to developing a new differential equation solver which is now incorporated in the BIOS module of MONDRIAN, we have demonstrated the relative efficiency of this in comparison with a previously employed differential equation solver and have compared the benefits with an alternative approach that restricted the solution to the case which required all the retardation factors to be equal. The comparison is based upon a 31 compartment biosphere model with an eight member radionuclide decay chain. Verification against the probabilistic assessment code MASCOT is also reported to further increase confidence.